1,720,985 research outputs found
Vibration of Thin-Walled Tubes in Thermal Environment
No full textVibrations induced by fast varying thermal gradients were first investigated by Boley in the Fifties with respect to the case of beams operating in extra-atmospheric microgravity environment. Indeed, spacecrafts and orbiting satellites crossing from the Earth’s shadow into sunlight experience rapid changes in the thermal loading due to the solar radiation. Such loading is responsible of time dependent bending moments and transverse shear forces on appendages and booms. Those are typically lightweight structures having high flexibility with low frequency and damping characteristic. The thermally-induced bending moment produces a sudden deflection of such flexible structures, accompanied by a change of sunlight incidence angle. These two set up the onset of vibrations with fluctuating moment that could not be correctly analyzed if the inertia effect and the coupling between temperature and strain fields are not taken into account. A correct comprehension of the phenomenon is of interest since thermally-induced vibrations may interfere with system operations of booms, often carrying a payload for measurement. In the worst cases thermal flutter, a self-excited vibration of increasing amplitudes, may lead to the failure of the structural member. In problems in which thermal effect induces deflections and vibrations of a slender body, thermal conductivity, material stiffness and mass density play an important role. If correctly selected these properties could improve the material robustness against deflection and oscillation. Hence, the question is if indeed does exist a certain combination of those material properties which can help to lower deflections and damp oscillations. In the proposed contribution a cantilever beam with a circular hollow cross-section is considered and the possibility to protect the beam from thermal effects by optimizing the structure of the cross-sectional wall is investigated. Some preliminary results seem encouraging and may pave the way for passive control of deflection and thermal flutter effects
Newton vs. Euler–Lagrange approach, or how and when beam equations are variational
Full text linkThere is a clear and compelling need to correctly write the equations of motion of structures in order to adequately describe their dynamics. Two routes, indeed very different from a philosophical standpoint, can be used in classical mechanics to derive such equations, namely the Newton vectorial approach (i.e., roughly, sum of forces equal to mass times acceleration) or the Euler–Lagrange variational formulation (i.e., roughly, stationarity of a certain functional). However, it is desirable that whichever derivation strategy is chosen, the equations are the same. Since many structures of interest often consist of slender and highly flexible beams operating in regimes of large displacement and large rotation, we restrict our attention to the Euler-Bernoulli assumptions with a generic initial configuration. In this setting, the question that arises is: What conditions must the constitutive assumptions satisfy in order for the equations of motion obtained by Newton’s approach to be identical to the Euler–Lagrange equations derived from an appropriate Lagrangian, natural or virtual, for any arbitrary initial configuration? The aim of this paper is to try to answer this basic question, which indeed does not have an immediate and simple answer, in particular as a consequence of the fact that bending moment could be related to two different notions of flexural curvature
From static buckling to nonlinear dynamics of circular rings
No full textThe dynamic buckling of circular rings is a pervasive instability problem with a major impact in various fields, such as structural, nuclear and offshore engineering, robotics, electromechanics, and biomechanics. This phenomenon may be simply seen as the complex motion that occurs deviating from the original circular shape under, for instance, any kind of time-dependent forcing load. Despite the fact that this topic has progressively gained importance since the mid-20th century, it seems that the same points have not been made completely clear. In fact, even some subtleties in the derivation of classical static buckling load may still give rise to misinterpretations and lead to misleading results. A fortiori, research concerning the nonlinear dynamics of rings still suffers the inherent difficulties associated with different possible analytical formulations of post-buckling dynamics. Advancement in this respect would be relevant, both from a theoretical and a practical point of view, since the applications are endless, with countless possibilities, especially in the biomedical and biotechnological fields: buckling-driven transformations of thin-film materials for applications in electronic microsystems, self-excited oscillations in collapsible tubes and pliable fluid-carrying shells, vocal-fold oscillations during phonation and snoring, pulse wave propagation in arteries, closure and reopening of pulmonary airways, stability of cardiac and venous valves during vascular surgery, stability of annuloplasty devices, flow-induced deformation and ultimate rupture of a cerebral aneurysm, and much more. The present article, in the framework of a critical review of the classic formulation of elastic ring buckling, proposes a straightforward approach for the nonlinear dynamics of an elastic ring that leads to a Mathieu–Duffing equation. In such a manner, some possible evolutions of the system under pulsing loads are analyzed and discussed, showing the inherent complexity of its dynamic behavior
Typical displacement behaviours of slope movements
No full textUnderstanding and quantifying the evolution of landslides are research topics that have always engaged researchers. Indeed, scientific literature provides a large number of contributions introducing and/or applying procedures, which are based on mechanical or phenomenological methods. The first ones are usually implemented to analyse the mechanical behaviour of a single complex phenomenon for which a consistent dataset is available. Phenomenological models are aimed at identifying common characteristics of landslides to be used for different purposes, such as forecasting the time of failure. This paper presents the implementation of a phenomenological model that allows the identification and quantification of well-defined dimensionless displacement trends for a large number of phenomena that are well documented in the literature. The analysed landslides involve different materials and are characterized by different stages of activity induced by seasonal and/or occasional triggering factors. The case studies include the well-known Vajont landslide, for which the obtained results show that the displacement trend was different from those usually characterizing occasionally reactivated landslides, since the beginning of the paroxysmal phase
Equilibrium of masonry-like vaults treated as unilateral membranes: Where mathematics meets history
No full textIn this paper, we study the equilibrium of masonry vaults, assuming that the material has infinite friction and no cohesion (i.e. it is No-Tension in the sense of Heyman). With Heyman's assumptions, the equilibrium of a structure composed of this ideal masonry material, can be studied with limit analysis. In particular, the present study is concerned with the application of the safe theorem of limit analysis to masonrylike vaults, that is, curved constructions modelled as continuous unilateral bodies. On allowing for singular stresses in the form of line or surface Dirac deltas, statically admissible stress fields concentrated on surfaces (and on their folds) lying inside the masonry, are considered. Such surface and line structures are unilateral membranes/arches, whose geometry is described a la Monge, and their equilibrium can be formulated in Pucher form. It is assumed that the load applied to the vault is carried by such a (possibly folded) membrane structure S. The geometry of the membrane S, that is of the support of the singularities, is not fixed, in the sense that it can be displaced and distorted, provided that one keeps it inside the masonry. Two particular case studies are analyzed to illustrate the method: a cross vaults of the Gothic Cathedral of Caserta, and a modern timbrel spiral stair built by the Guastavinos in New York
Nonlocal vibration analysis of a nonuniform carbon nanotube with elastic constraints and an attached mass
No full textHere, we consider the free vibration of a tapered beam modeling nonuniform single-walled carbon nanotubes, i.e., nanocones. The beam is clamped at one end and elastically restrained at the other, where a concentrated mass is also located. The equation of motion and relevant boundary conditions are written considering nonlocal effects. To compute the natural frequencies, the differential quadrature method (DQM) is applied. The influence of the small-scale parameter, taper ratio coefficient, and added mass on the first natural frequency is investigated and discussed. Some numerical examples are provided to verify the accuracy and validity of the proposed method, and numerical results are compared to those obtained from exact solution. Since the numerical results are in excellent agreement with the exact solution, we argue that DQM provides a simple and powerful tool that can also be used for the free vibration analysis of carbon nanocones with general boundary conditions for which closed-form solutions are not available in the literature
Static analysis of a double-cap masonry dome
No full textThe present work is focused on the analysis of the double-cap dome of St. Januarius Chapel, in Naples (Italy). Three different approaches based on the limit analysis for unilateral (no-tension) material has been applied to evaluate the dome stability. In the first approach, the overall stability of the dome has been investigated through a method of graphical statics. The method is a generalization of the “thrust line analysis” used for arches and consists in finding a purely compressed membrane in equilibrium with the external loads and entirely contained in the thickness of the dome, in the spirit of safe theorem. In the second approach, which is concerned with the equilibrium of domes and vaults, a thrust surface in equilibrium with the assigned external loads is found by numerically solving the Pucher’s differential equation. This latter is nothing but the equilibrium of the unknown thrust surface along the direction of vertical, i.e. gravitational, loads, where generalized stresses are conveniently projected on the platform, that is in the horizontal plane. Again in the spirit of the safe theorem, the thrust surface must be entirely contained within the volume of the structure. The solution procedure is based on the finite difference technique and has been implemented in a Mathematica-based code. Finally, in the third approach, a three-dimensional rigid block model with no-tension, frictional interfaces is employed. The formulation and the solution procedure of the underlying limit analysis problem has been implemented in a MATLAB-based tool equipped with a graphical user interface. The obtained results allow to state that the dome, under ordinary load conditions, is safe
Computational modeling of the dynamics of active sunscreens with tensegrity architecture
No full textRecent studies have investigated the use of tensegrity structures for the construction of active solar façades of Energy Efficient Buildings. In this paper we simulate the dynamics of shading screens with tensegrity architecture through an in-house developed code that handles rigidity constraints on the deformation of the bars. We present numerical results illustrating the dynamic response of a tensegrity solar façade and its morphing capabilities, which require minimal storage of internal energy
INVESTIGATING THE EVOLUTION OF LANDSLIDES VIA DIMENSIONLESS DISPLACEMENT TRENDS
No full textUnderstanding and quantifying the time evolution of landslides has always engaged researchers because of the consequences of such phenomena on the stability of buildings and infrastructure, and the loss of life. Consider, e.g., the catastrophic Vajont landslide in northern Italy in 1963 which caused great damage and the death of 1,917 people. The scientific literature reports both mechanical and phenomenological approaches to analyzing landslide evolution. This paper aims to fill the gap between such approaches by introducing a geometric stability analysis of experimentally measured displacements trends. The proposed analysis organizes the experimental data of a given event into a dimensionless chart. The overall set of displacement data is partitioned into a sequence of activity stages associated with different triggering factors. This preliminary, but fundamental step, allows recognition of the common growth properties of different landslide displacements, independently of the volume of the main moving body, the material composition, and so on. The second step consists of a powerlaw regularization of the experimental data that allows the computing of time derivatives of the dimensionless cumulative displacements up to the third order (velocity, acceleration and second acceleration, or jerk). The approximating functions are used to understand and quantify the behavior of an experimentally monitored landslide event, by tracking its activity stages into a stability chart that accounts for five different regimes. The robustness of the proposed procedure is demonstrated through application to many well-documented case studies
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